Please see the attached image which shows an error/information message I am seeing regularly since upgrading to Yosemite. I don't know which website is asking for Java, as there is a different site showing in Safari each time I see it, but I do know that I am using the latest version of JRE so it's not clear why this message is being shown.
Can someone please advise me the best way to check what process is generating this, and how I can fix it?